The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have
The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have
The second sum is simply the sum of N ones:
So, the final result is
which ends the proof.
Answer:
The number of ways the grasshopper can reach the desired destination are 9 ways
Step-by-step explanation:
The directions in which the grasshopper can jump are;
One block north and one block west
By counting, we have;
The number of possible ways are through blocks
1) 1, 2, 5, 6, 8, 10
2) 1, 2, 5, 6, 8, 9
3) 1, 2, 5, 6, 7, 9
4) 1, 2, 3, 6, 8, 10
5) 1, 2, 3, 6, 8, 9
6) 1, 2, 3, 6, 7, 9
7) 1, 2, 3, 4, 7, 9
8) 15, 14, 16, 12, 11, 10
9) 12, 13, 16, 12, 11, 10
Therefore, there 9 ways the grasshopper can reach the desired destination.
Answer:
length is 28.86ft
width= 4.12ft
Step-by-step explanation:
<h2>
This problem bothers on the mensuration of solid shapes, a rectangular prism.</h2>
The storage space takes the shape of a rectangular prism, and we are required to find the width and length of the storage space.
let the width of the basement be "w"
Given data
volume v=
length l = 
width w= 
height h= 
We know that the expression for the volume of a rectangular prism is
substituting our data we have to find "w"
dividing both sides by 35 we have
find the square root of both sides we have
since we know that length= 7w and width = w , we can substitute our value for w and find the length and width
Answer:
i dont knwo
Step-by-step explanation:
Let the number be n. Then 2(n-10) = 6n + 14.
Multiplying out the left side, 2n - 20 = 6n + 14. Thus, -34=4n, and n = -17/2.
